Associated $Z$ + $J/\psi$ production as a probe of multiparton interactions in the forward region

Using LHCb data from proton-proton collisions at 13 TeV, this study demonstrates that associated $Z$ + $J/\psi$ production in the forward region is dominated by multiparton interactions, yielding an effective cross-section of $16.6 \pm 4.7$ mb that provides new constraints on the proton's transverse spatial structure at small Bjorken-$x$.

The Gist

Imagine the proton, the tiny particle at the heart of every atom, not as a solid marble, but as a bustling, three-dimensional city. Inside this city live "partons" (quarks and gluons), which are like the citizens. We know a lot about how these citizens move forward and backward (their momentum), but we know very little about how they are spread out across the width of the city (their transverse spatial distribution).

This paper from the LHCb experiment at CERN is like sending a high-speed camera into that city to take a snapshot of how these citizens interact when two proton-cities crash into each other at nearly the speed of light.

Here is the story of what they found, explained simply:

The Big Crash and the "Double-Date" Theory

When two protons smash together at the Large Hadron Collider (LHC), it's usually expected that they will interact just once. Think of this as two people bumping into each other in a crowded hallway and shaking hands. This is called Single-Parton Scattering (SPS).

However, the scientists were looking for something rarer: a "double date." This is where, in a single crash, two separate pairs of citizens interact independently at the same time. This is called Double-Parton Scattering (DPS). It's like two people bumping into each other, shaking hands, and at the exact same moment, their two friends standing right next to them also bump into each other and shake hands.

The Experiment: Catching a Rare Pair

To find evidence of this "double date," the LHCb team looked for a very specific and rare combination of particles produced in the crash:

1. A Z boson (a heavy particle that acts like a messenger of the weak force).
2. A J/ψ meson (a particle made of a charm quark and an anti-charm quark).

They looked for these in the "forward region," which is like looking at the edge of the city rather than the center. This is a special place where the "citizens" (partons) are moving very slowly relative to the speed of the proton, a region scientists call "small-x."

The Surprise: It's Not Just a Simple Bump

The team collected data from 2016 to 2018 (about 5.1 "inverse femtobarns" of data, which is a huge amount of collisions). They found 56 clear examples of this Z + J/ψ pair being created.

When they compared this to the "Single-Parton Scattering" theory (the idea that it was just one big interaction), the theory predicted they should only see about 0.1 events. Instead, they saw 5.5.

The Analogy: Imagine you are trying to guess how many times two people will shake hands in a crowd. Your math says it should happen once a year. But you walk in and see it happening five times in an hour. You realize your math was missing something: people are shaking hands in pairs simultaneously, not just one big group interaction.

The data showed that the "double date" (DPS) is the dominant way this happens in this specific region. The single interaction (SPS) is just too weak to explain what they saw.

Measuring the "City Layout"

By studying how often these double interactions happen, the scientists could calculate a number called $\sigma_{eff}$ (sigma-eff).

Think of $\sigma_{eff}$ as a measure of how "crowded" or "spread out" the citizens are in the proton city.

• If the citizens are tightly packed in the center, the double interactions happen often, and the number is small.
• If they are spread out, the number is larger.

The LHCb team calculated this number to be 16.6 mb (millibarns). This number helps physicists understand the physical size and shape of the proton's interior.

Why This Matters

This is a unique discovery because it combines two things that haven't been studied together before:

1. High Energy: The Z boson is very heavy, providing a "hard" scale (like a high-resolution camera).
2. Forward Region: They looked at the edge of the collision where the "small-x" partons live.

Previous studies looked at either the center (where quarks dominate) or the edge with lower energy (where gluons dominate). This study bridges the gap, showing that even in this high-energy, edge-of-the-city environment, the "double interaction" rule still holds true.

The Bottom Line

The paper concludes that in the forward region of proton collisions, the process of creating a Z boson and a J/ψ meson is almost entirely driven by two independent interactions happening at once, rather than one big interaction.

This gives scientists a new, direct way to map the 3D structure of the proton, confirming that the "effective cross-section" (the measure of how partons overlap) seems to be roughly the same whether you are looking at the center of the proton or the edge, and whether you are using high or low energy. It's a new piece of the puzzle in understanding the fundamental architecture of matter.

Technical Summary

Technical Summary: Associated $Z + J/\psi$ Production as a Probe of Multiparton Interactions in the Forward Region

Problem and Motivation
The three-dimensional structure of the proton, specifically the transverse spatial distribution of its constituent partons, remains a central topic in Quantum Chromodynamics (QCD). While Parton Distribution Functions (PDFs) constrain longitudinal momentum, experimental data on transverse distributions, including Transverse-Momentum-Dependent (TMD) distributions, are limited. Double-Parton Scattering (DPS), where two independent hard interactions occur in a single proton-proton collision, offers sensitivity to this transverse structure. The effective cross-section, $\sigma_{\text{eff}}$, derived from DPS measurements, encodes the transverse overlap of partons.

Existing $\sigma_{\text{eff}}$ measurements are largely consistent but predominantly probe quark-dominated mechanisms at central rapidities. Theoretical studies suggest $\sigma_{\text{eff}}$ may depend on the underlying partonic subprocesses (valence quarks vs. gluons) and the hard scale ($Q^2$). There is a need for complementary studies in gluon-rich kinematic regimes characterized by small Bjorken-$x$ and high hard scales. The associated production of a $Z$ boson and a prompt $J/\psi$ meson in the forward region offers a unique laboratory for this: it combines the electroweak hard scale of the $Z$ mass ($Q^2 \sim m_Z^2$) with the forward rapidity coverage of the LHCb detector, probing a region of $x \sim 10^{-4}$ previously unconstrained experimentally. In this regime, Single-Parton Scattering (SPS) is expected to be suppressed due to the asymmetric parton configuration required, enhancing sensitivity to multiparton interactions.

Methodology
The analysis utilizes proton-proton collision data collected by the LHCb detector at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of $5.1 \text{ fb}^{-1}$.

• Event Selection: Candidates are reconstructed in the final state containing two pairs of oppositely charged muons, corresponding to $Z \to \mu^+\mu^-$ and prompt $J/\psi \to \mu^+\mu^-$. The selection is confined to the LHCb forward acceptance ($2 < \eta < 5$).
  • Fiducial Region: Defined by $60 < m_{\mu^+\mu^-} < 120 \text{ GeV}/c^2$ and $p_T > 20 \text{ GeV}/c$ for $Z$-decay muons ($2 < \eta < 4.5$); and $0 < p_T^{J/\psi} < 14 \text{ GeV}/c$ and $2 < y^{J/\psi} < 4.5$ for the prompt $J/\psi$.
  • Vertexing: A kinematic fit constraining the $Z$ and $J/\psi$ candidates to a common production vertex is applied to reject pileup backgrounds (where candidates originate from different collisions in the same bunch crossing) and non-prompt $J/\psi$ from $b$-hadron decays.
• Signal Extraction: Signal yields are extracted via a simultaneous fit to the invariant mass distributions of the $Z$ and $J/\psi$ candidates. Signal shapes are modeled using double-sided Crystal Ball functions calibrated with control samples, while combinatorial backgrounds are described by smooth exponential functions. The sPlot technique is used to subtract background and assign per-candidate weights.
• Cross-Section Determination: The fiducial cross-section is calculated using the efficiency-corrected signal yield, integrated luminosity, and branching fractions. Total efficiency is factorized into acceptance, reconstruction/selection, particle identification (PID), and trigger components, determined via simulation and corrected with control samples.
• Theoretical Comparison: The SPS contribution is evaluated using the HELAC-Onia package (including color-singlet and color-octet channels). The DPS contribution is estimated within the standard factorized framework using single-$Z$ and single-$J/\psi$ cross-sections as inputs.

Key Results

• Fiducial Cross-Section: The measured fiducial cross-section for associated $Z + J/\psi$ production is:
  $$\sigma_{Z+J/\psi} = 5.5 \pm 1.5 \text{ (stat)} \pm 0.4 \text{ (syst)} \pm 0.1 \text{ (lumi)} \text{ pb}$$
• SPS vs. DPS: The measured value significantly exceeds the SPS theoretical prediction within the same fiducial region, which is calculated to be $\sigma_{Z+J/\psi}^{\text{SPS}} = 0.10 \pm 0.08 \text{ pb}$. This discrepancy indicates that SPS alone cannot describe the process in this phase space and that multiparton interactions dominate.
• Effective Cross-Section ($\sigma_{\text{eff}}$): Interpreting the excess as a DPS contribution within the standard factorized framework yields:
  $$\sigma_{\text{eff}} = 16.6 \pm 4.4 \text{ (stat)} \pm 1.5 \text{ (syst)} \text{ mb}$$
  The systematic uncertainty includes contributions from the measured cross-section, single-particle cross-section inputs, and SPS subtraction.
• Differential Distributions: Differential cross-sections as functions of $y_{J/\psi}$ and $y_Z$ are presented. The data are compatible with SPS+DPS predictions for $\sigma_{\text{eff}}$ values in the range of 10–20 mb. No strong additional kinematic correlations beyond those captured by the factorized DPS framework are observed.

Significance and Claims
The paper claims that this measurement provides the first experimental constraint on multiparton interactions in a kinematic regime characterized simultaneously by small Bjorken-$x$ ($x \sim 10^{-4}$) and a high electroweak hard scale ($Q^2 \sim m_Z^2$).

The extracted $\sigma_{\text{eff}}$ value is consistent with measurements from central rapidity (electroweak boson and high-multiplicity jet processes) and forward rapidity (quarkonium-pair production) experiments, despite the vastly different kinematic regimes and partonic compositions. This observation provides experimental evidence that the effective transverse scale governing multiparton interactions remains approximately universal across a wide range of $x$ values, hard scales, and partonic initial states. The result extends existing constraints into the small-$x$, high-$Q^2$ regime, offering a new benchmark for modeling DPS and constraining the transverse spatial structure of the proton.